Otto Graham also won ten division titles (some of them Conference titles since there were no "Divisions" in his day) according to his Canton Web Page, so Brady would be tied for the "All Time" record; not shabby company. Otto Graham is, BTW, considered by Canton as part of the "Modern Era," even though he played part of his career in the old AAFC. Go argue with them about that, not me.
Steve Young won nine division titles. Staubach won eight. Manning now has nine. The others that have been mentioned either didn't play long enough or didn't win their Conference(old days)/Division enough times.
As for League Titles ("Beyond" the Topic but not quite "Off" the topic):
Graham (putting aside the question of whether or not you accept Canton's definition) holds the record for a Modern Era QB with seven titles.
Bart Starr, whose career overlapped the Super Bowl era, holds the record for players who played part of their career in the SB era at five League titles (three before, two during). My personal view is that he holds this record for Modern Era QB's, but that's just my view, since as far as Canton is concerned it belongs to Graham.
Bradshaw and Montana, as we all know, hold the record for players who played their entire career in the Super Bowl Era at four League titles.